US8502731B2 - System and method for moving target detection - Google Patents
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- US8502731B2 US8502731B2 US13/008,549 US201113008549A US8502731B2 US 8502731 B2 US8502731 B2 US 8502731B2 US 201113008549 A US201113008549 A US 201113008549A US 8502731 B2 US8502731 B2 US 8502731B2
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/887—Radar or analogous systems specially adapted for specific applications for detection of concealed objects, e.g. contraband or weapons
- G01S13/888—Radar or analogous systems specially adapted for specific applications for detection of concealed objects, e.g. contraband or weapons through wall detection
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/0209—Systems with very large relative bandwidth, i.e. larger than 10 %, e.g. baseband, pulse, carrier-free, ultrawideband
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/52—Discriminating between fixed and moving objects or between objects moving at different speeds
- G01S13/538—Discriminating between fixed and moving objects or between objects moving at different speeds eliminating objects that have not moved between successive antenna scans, e.g. area MTi
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/66—Radar-tracking systems; Analogous systems
- G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
- G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
- G01S13/9021—SAR image post-processing techniques
- G01S13/9029—SAR image post-processing techniques specially adapted for moving target detection within a single SAR image or within multiple SAR images taken at the same time
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/28—Details of pulse systems
- G01S7/285—Receivers
- G01S7/292—Extracting wanted echo-signals
- G01S7/2923—Extracting wanted echo-signals based on data belonging to a number of consecutive radar periods
Definitions
- the embodiments herein generally relate to detection, and more particularly, to detection of moving targets.
- UWB ultrawideband
- ARL Technical Report 5037 discloses a description of a moving target indication (MTI) processing approach to detect and track slow-moving targets inside buildings, which successfully detected moving targets (MTs) from data collected by a low-frequency, ultrawideband radar.
- MMI moving target indication
- MTI processing algorithms include change detection (CD), used to identify the MT signature; automatic target detection (ATD), used to eliminate imaging artifacts and potential false alarms due to target multi-bounce effects; clustering, used to identify a centroid for each cluster in the ATD output images; and tracking, used to establish a trajectory of the MT.
- CD change detection
- ATD automatic target detection
- clustering used to identify a centroid for each cluster in the ATD output images
- tracking used to establish a trajectory of the MT.
- the algorithms in the MTI processing formulation can be implemented in a real-time or near real-time system; however, a person-in-the-loop is needed to select input parameters for the k-Means clustering algorithm.
- the number of clusters input into the k-Means routine is unknown and requires manual selection.
- two techniques are investigated that automatically determine the number of clusters: the knee-point (KP) algorithm and the recursive pixel finding (RPF) algorithm.
- KP knee-point
- RPF recursive pixel finding
- the KP algorithm is a well-known heuristic approach for determining the number of clusters.
- the RPF algorithm is analogous to the image processing, pixel labeling procedure. Both routines processed data collected by low-frequency, ultrawideband radar.
- a time-domain approach to MTI was considered as an alternative to a frequency-domain approach, i.e., Doppler processing, since a very small Doppler shift in backscattered frequency is generated due to (1) the slow motion of the mover and (2) the low frequency needed to penetrate through the wall.
- the reported time-domain processing algorithms are based on the change detection (CD) paradigm, which is inherently similar to clutter cancellation.
- CD change detection
- the Synchronous Impulse Reconstructive (SIRE) radar remains stationary and generates a set of images for a region of interest (ROI). Each image in the set is formed every two-thirds of a second.
- the stationary objects in the building remain in the same location in each image; however, moving personnel will be at different locations.
- the moving personnel can be detected by subtracting adjacent images in the set, thereby eliminating the stationary objects and identifying the MT signature.
- Additional processing is needed to enhance the MT signature and includes a constant false alarm rate (CFAR) algorithm, morphological processing, k-Means clustering, and a tracking algorithm.
- CFAR and morphological processing are approaches used to eliminate imaging artifacts and potential false alarms due to target multi-bounce effects.
- the k-Means clustering algorithm is used to identify centroids for given input clusters, where the clusters are produced by the CFAR and morphological processing algorithms.
- the tracker is used to establish a trajectory of the MT based on the input centroids.
- Synchronous Impulse Reconstruction (SIRE) Radar is a low-frequency, ultra-wideband (UWB) radar having a frequency range of 300 MHz ⁇ 3 GHz.
- An example of SIRE system is illustrated in FIG. 1 , showing 2 transmitters and 16 receivers in an antenna array 2 m wide having an average power of 5 mW with a downrange swath is 10-meters and a downrange resolution is 0.056 meters.
- a preferred embodiment of the present invention comprises a cluster prediction algorithm for a system to automatically detect and track moving personnel inside buildings.
- the novel cluster prediction algorithm inter alia, 1) automatically determines the number of clusters in an image (where each cluster corresponds to a potential moving target), 2) reduces false alarms, and 3) automates the entire moving target indication (MTI) system.
- MTI moving target indication
- This fully automated MTI system can be utilized to detect and track hostile personnel, enemy snipers, or hostages inside buildings.
- the MTI system could also be used for commercial applications that include: 1) law enforcement, 2) search and rescue, 3) building surveillance, 4) vehicle tracking on highways or in remote locations.
- the MTI system effectively combines several algorithms in a novel way to image slow and fast moving personnel from 6 m to 30 m inside building structures.
- the MTI system has successfully demonstrated detection capabilities of personnel walking inside wood and cinderblock buildings.
- the moving target indication (MTI) system is comprised of two main components.
- the first component detects potential moving targets by generating a time series of binary images that contain clusters.
- the second component of the MTI system tracks the centroid of each cluster thereby indicating any moving target in the building. Both components have been studied individually in past research, but could not be combined since the second component requires manual input. Specifically, the number of clusters in the binary images (output of the first component) is unknown and must be manually input into the second component of the system.
- the cluster prediction algorithm i) automatically determines the number of clusters present in the binary images, ii) reduces false alarms in the binary images, iii) combines the first and second components of the MTI system thereby automating the entire MTI system.
- the cluster prediction algorithm is a novel, necessary, and unique contribution to the MTI system.
- a preferred method of detecting moving targets comprises transmitting electromagnetic waves rays from a plurality of transmitters at sequential; receiving reflected waves into a plurality of receivers after each transmission; the compilation of the reflected waves from the plurality of receivers for each transmission representing a data frame; forming a signal that monitors changes between the two sets of frames; at least one processor operating to process and compare frames; forming a difference image using a back-projection algorithm; scanning the difference image using a constant false alarm rate (CFAR) window; the CFAR window scanning the entire difference image and identifying a list of points of interest and eliminating the sidelobe artifacts present in the difference image thereby creating CFAR images; processing the CFAR images using morphological processing to create a morphological image; determining the number of clusters present in the morphological image; using K-means clustering to indicate the centroid of each cluster; and tracking using a Kalman filter.
- CFAR constant false alarm rate
- a preferred embodiment system for detecting moving targets comprises a plurality of M transmitters, a plurality of receivers, and at least one memory, the transmitters operating in sequence to transmit electromagnetic waves rays sequentially; the receivers receiving reflected waves after each transmission; the compilation of the reflected waves from the plurality of receivers for each transmission representing a data frame; at least one processor operating to perform the steps of: forming a signal that monitors changes between the two sets of frames; at least one processor operating to process and compare frames; forming a difference image using a back-projection algorithm; scanning the difference image using a constant false alarm rate (CFAR) window; the CFAR window scanning the entire difference image and identifying a list of points of interest and eliminating the sidelobe artifacts present in the difference image thereby creating CFAR images; processing the CFAR images using morphological processing to create a morphological image; determining the number of clusters present in the morphological image; using K-means clustering to indicate the centroid of each cluster; and tracking using a Kalman
- the colors represent a decibel range which ranges from red to blue, red being the strongest signal and blue being the weakest.
- FIG. 1 illustrates a schematic diagram of a vehicle having a synchronous Impulse Reconstruction (SIRE) Radar mounted thereon.
- SIRE synchronous Impulse Reconstruction
- FIG. 2 is a block diagram showing a moving target indication system for data collected by a low-frequency UWB radar with correlated illustrations.
- FIG. 3 is a block diagram of a is a block diagram showing a moving target indication system for data collected by a low-frequency UWB radar including cluster prediction.
- FIG. 4 illustrates two SAR images (a and b) of a target area with a moving target present; the location of the mover is unknown
- FIG. 5 is an illustration of a difference image generated by applying change detection to the SAR images of FIG. 4 , wherein the moving target signature is identifiable.
- FIG. 6 schematically illustrates an example of a CFAR window comprising an inner, guard and outer window.
- FIG. 7 is a schematic illustration of a CFAR window placed over the MT signature, where the inner window is overlaid on the MT signature and the outer window covers the background of the local area.
- the inner window contains pixels with higher energy compared with the pixels contained in the outer window.
- FIG. 8A is an illustration comprising 6 ATR images with 2 clusters present per ATR image and wherein each “Error Line” corresponds to 1 image;
- FIG. 8B is a graphical depiction of a knee point algorithm based upon FIG. 8A .
- FIG. 9A is a schematic illustration revealing themorphological image that contains points of interest (POIs).
- PIs points of interest
- FIG. 9B is an illustration based upon FIG. 9A when these images are input into a clustering algorithm, two clusters are identified; the clusters and corresponding centroids are shown.
- FIG. 10 is block diagram of the k-Means algorithm.
- FIG. 13 is a schematic graphical illustration showing the knee point for the six images of FIG. 12 .
- FIG. 15 is a schematic block diagram of the adaptive Knee point (KP) algorithm.
- the preferred embodiment moving target indication (MTI) system is comprised of two main components.
- the first component detects potential moving targets by generating a time series of binary images that contain clusters.
- the second component of the MTI system tracks the centroid of each cluster thereby indicating any moving target in the building.
- Both components have been studied individually in past research reported in A. Martone, et al., “Automatic Through the Wall Detection of Moving Targets using Low-Frequency Ultra-Wideband Radar,” Proceedings of the IEEE international radar conference, Washington, D.C., May 2010, A. Martone, et al., “An Analysis of Clustering Tools for Moving Target Indication; ARL-TN-5037; U.S. Army Research Laboratory: Adelphi, Md., November 2009, A.
- the cluster prediction algorithm i) automatically determines the number of clusters present in the binary images, ii) reduces false alarms in the binary images, iii) combines the first and second components of the MTI system thereby automating the entire MTI system.
- the cluster prediction algorithm is a novel, necessary, and unique contribution to the MTI system.
- a time-domain processing system that utilizes a low-frequency, ultra-wideband (UWB) radar.
- UWB ultra-wideband
- a low-frequency, UWB radar is desired since the low-frequency transmit pulse is capable of penetrating the wall, as reported in Farwell, M., et al., “Sense through the wall system development and design considerations,” J. of the Franklin Institute September 2008, 345 (6), 570-591, hereby incorporated by reference, and the ultra-wideband corresponds to a high range resolution that gives the capability to better locate the moving target.
- the time-domain approach to moving target indication (MTI) is utilized as an alternative to a frequency-domain approach, i.e. Doppler processing, since a very small Doppler shift in backscattered frequency is generated due to: 1) the slow motion of the mover and 2) the low frequency needed to penetrate the wall.
- the MTI system is shown in FIG. 3 .
- the MTI processing system consists of the following processing routines: change detection, image formation via a specially adapted version of the back-projection algorithm, constant false alarm rate (CFAR) processing, morphological processing, cluster prediction, k-Means clustering, and tracking via the Kalman filter.
- CFAR constant false alarm rate
- morphological processing cluster prediction
- cluster prediction cluster prediction
- k-Means clustering k-Means clustering
- tracking via the Kalman filter a novel contribution to the MTI processing system.
- the cluster prediction algorithm i) automatically determines the number of clusters present in the binary images, ii) reduces false alarms in the binary images, iii) combines the detection and tracking components of the MTI system thereby automating the entire system.
- the constituent radar in our MTI system remains stationary and measures the energy reflected from an area under surveillance.
- Downrange profiles are measured and buffered by each receive channel for a single set of transmit pulses. Since the transmitters fire in sequence, M downrange profiles are effectively buffered (one for each transmitter) from each receive channel, and the time required to assemble these profiles represents one frame of data. After buffering the data from one frame, another M downrange profiles are collected from each receive channel for the next frame of data.
- r represents the downrange index
- i represents the time index
- j represents the transmitter index
- k represents the receiver index.
- a signal is formed that monitors changes between the two sets of downrange profiles measured at time i and time i+1 using transmitter j and receiver k; hence, the name of the model is a “change detection” (CD) paradigm.
- the difference signal, ⁇ dot over (f) ⁇ i,j,k (r) (corresponding to the derivative in time), is then input to an image formation routine, in this case a time-domain back-projection procedure, resulting in the output difference image,
- g(i,j,k) is a scaling function.
- SAR Image 1 I 1 (x,y)
- SAR Image 2 I 2 (x,y)
- SAR Image 2 I 2 (x,y)
- SAR images contain several artifacts making it difficult to identify the moving target.
- the moving target is located by applying change detection.
- the resulting difference image is shown in FIG. 5 . It is clear from the difference image that most of the artifacts due to stationary clutter have been eliminated and the resulting MT signature is identified.
- CFAR is a well-established approach to eliminating potential false alarms.
- the algorithm performs a test of local contrast that is designed to achieve a constant false alarm rate as reported in Khan, P. P. & Kassam, S. A., “Analysis of CFAR Processors in Homogeneous Background,” IEEE Transactions on Aerospace and Electronic Systems July 1988, 24 (4), 427-445, hereby incorporated by reference.
- I diff x,y
- a CFAR window is used to scan the difference image and test for the MT signature.
- An example of a CFAR window is shown in FIG.
- I X and I Y are the inner windows' cross-range and range dimensions, respectively; G X and G Y are the guard windows' cross-range and range dimensions; and O X and O Y are the outer windows' cross-range and range dimensions.
- the inner window dimensions are designed so that it is overlaid on the MT signature.
- the outer window dimensions are designed to be superimposed on the local background.
- the guard window is used as a buffer between the inner and outer windows and ensures that large pixel values due to target sidelobes are not captured by the outer window. For example, consider the window that is placed in the difference image shown in FIG. 7 . As is illustrated in the figure, the inner window is overlaid on the MT signature pixels and the outer window is overlaid on the local background pixels.
- the dimensions of the inner window constitute a small rectangular shape, which is different from the elliptical patterns of the MT signatures.
- the rectangular shape is chosen since it is small enough to fit over the MT signatures.
- the small rectangular window is used as an alternative to an elliptical window since the size and shape of the pattern of the moving target changes depending on the range and cross-range of the mover's position.
- the CFAR window is placed in the difference image of size (500,500) and moved pixel by pixel over the entire difference image. Let the center of the CFAR window be positioned at coordinates (X, Y) in the difference image, where X ⁇ X /2 ⁇ , . . . (500 ⁇ O X /2 ⁇ ) ⁇ and Y ⁇ O Y /2 ⁇ , . . . (500 ⁇ O Y /2 ⁇ ) ⁇ .
- ⁇ x ⁇ denotes the largest integer less than x for x>0 (i.e., floor), and ⁇ x ⁇ denotes the smallest integer greater than x for x>0 (i.e., ceiling).
- the CFAR algorithm indicates an MT signature if the sum of the energy in the inner window is larger than the sum of the energy in the outer window. This is shown in FIG. 7 , where the energy of the pixels in the inner window is larger then the energy of the pixels in the outer window.
- the inner window to outer window energy ratio is defined as
- ⁇ ⁇ ( P ( l , k ) ) ⁇ P ( l , k ) , P ( l , k ) > ⁇ ⁇ , P ( l , k ) ⁇ ⁇ , ( 5 )
- ⁇ max(I diff (x,y))/2
- max(I diff (x,y)) is the maximum pixel magnitude in the difference image.
- the function ⁇ (P (l,k) ) is used to adjust the image background and require that the magnitude of each pixel is above the threshold defined by ⁇ , which is done to prevent errors due to division by very small numbers. Division by very small numbers artificially inflates the ratio defined by equation 3 and causes false positives.
- the threshold ⁇ was chosen based on the observations of the sidelobes corresponding to the MT signature, which are typically less than max(I diff (x,y))/2 in magnitude. This choice of ⁇ eliminates the sidelobes by blending them into the background of the difference image.
- the sum of the energy in the outer window is defined as
- ⁇ o E W - E I + G , ⁇
- the CFAR window scans the entire difference image and a list of POIs are identified. For example, consider the difference image and CFAR image of FIGS. 8A and 8B . The difference image is input into the CFAR algorithm and the CFAR image is output. The red cluster in the CFAR image corresponds to a group of POIs. This example illustrates that the CFAR algorithm identifies the MT signature and eliminates the sidelobe artifacts present in the difference image.
- morphological processing is applied to further refine the number of clusters present in the CFAR images.
- the morphological processing considered implements a dilation and erosion procedure. Dilation is used to grow the POI clusters and erosion is used to shrink the POI clusters.
- the dilation process is designed to connect clusters in close proximity by dilating all pixels in each CFAR image. For dilation define a 17 ⁇ 17 dilation window ⁇ d is defined as:
- the 17 ⁇ 17 dilation window size was chosen to connect clusters separated by a distance of 0.68 m or less (this distance was chosen based on observations of the clusters in the CFAR images). Similar to CFAR, a dilation test statistic is defined:
- an 8 pixel buffer exists along the edge of the CFAR image (i.e. not enough samples exist at the edges of the image).
- There exist i 1, . . . N ⁇ 1 dilation images; one for each CFAR image.
- the k-Means algorithm is referenced Wilpon, J., et al., “A Modified K-means Clustering Algorithm for Use in Isolated Work Recognition,” IEEE Transactions on Acoustics, Speech and Signal Processing vol. 33, no. 3, July 1985, 587-594, hereby incorporated by reference.
- the k-Means algorithm requires the number of clusters present in the morphological images and is provided by the cluster prediction algorithm described in the section entitled Cluster Prediction Algorithm.
- a cluster is defined as a group of one or more POIs that are close to one another in the image. The total number of clusters present in the morphological image referred to as T. For example, consider the POIs in FIG.
- FIG. 9A a morphological image where each POI corresponds to a blue diamond.
- FIG. 9B The POIs connected to each other form a cluster as illustrated in FIG. 9B .
- the k-Means algorithm is used to indicate the centroid of each cluster.
- the k-Means algorithm identifies the centroids of the POIs by an iterative procedure. This iterative procedure minimizes the square-error between centroid estimates and their corresponding POIs. It should be noted that the clusters identified by the clustering algorithm are not unique and it is possible that the centroid locations differ for different iterations of the clustering algorithm.
- a block diagram of the k-Means algorithm is shown in FIG. 10 .
- the input morphological image contains a set of M POI vectors, where each vector is of size two and contains range and cross-range position information.
- the k-Means algorithm begins by randomly generating T mean vectors and defining each mean vector to be a centroid location. Note that, at this point, T is unknown and must be manually defined. The adaptive KP algorithm can be leveraged to automatically determine T. The next step of the k-Means algorithm determines the mean vector nearest to each POI using the Euclidean distance measure. An error (offset) is then estimated between the mean vector and nearest POIs using the sum of squares (SOS) error criteria as referenced in Duta, R, et al., “Pattern Classification,” 2nd ed.
- SOS sum of squares
- This SOS error criterion is a measure of variance between the POI vectors and the nearest mean vectors and must be minimized. Once minimized, the SOS error indicates the final centroid estimates represented by the mean vectors. For example, consider the morphological image in FIG. 11 . In this example, two mean vectors were randomly generated and indicated by the red diamond and black star. As the k-Means algorithm iterates, several centroids are estimated. Each newly generated estimate corresponds to a smaller SOS error.
- the red line indicates progression of the first mean vector and the black line indicates progression of the second mean vector. Multiple iterations are needed to minimize the error between the POIs and nearest mean vectors.
- the tracker algorithm is intended to reduce the number of false alarms and segregate targets from both clutter and one another as they move inside a building.
- the centroids generated by the clustering algorithm serve as inputs to the tracker; so it is possible to have multiple tracker inputs even when a single moving target is present. These centroids may indicate the true position of a moving target or false alarms.
- the tracker estimates the correlation between each centroid and the existing tracks and then associates the existing tracks with the most highly correlated (i.e., most reasonable) centroid. Non-assigned centroids are used to initiate new tracks and outdated tracks are deleted.
- a Kalman filter determines the present track position and predicts the next measurement.
- the Knee-Point (KP) algorithm (i.e. non-adaptive) is one approach to automatically determine T for a particular morphological image.
- the KP algorithm is a heuristic approach used to determine the optimal number of clusters as referenced in Thorndike, R. “Who belongs in the family?” Psychometrika December 1953, 18 (4), 267-276, and Zhao, Q. et al. “Knee Point Detection on Bayesian Information Criteria,” Proceedings of the 20th IEEE International Conference on Tools with Artificial Intelligence, vol. 2, November 2008, 431-438, hereby incorporated by reference.
- the KP algorithm begins by repeating the k-Means algorithm for many different cluster number choices, where the maximum cluster number is denoted by C.
- the ambiguity of the NMSOS errors motivates the need to adapt the KP algorithm to include training information.
- the training information consists of NMSOS errors obtained by the KP-algorithm.
- each NMSOS error in the training set contains a label, ⁇ 1, . . . C ⁇ , indicating T.
- FIG. 15 A block diagram of the adaptive KP algorithm is shown in FIG. 15 .
- the k-Nearest Neighbor (k-NN) classifier then utilizes the training set to automatically determine the number of clusters, i.e. N p , corresponding to the morphological image.
- the k-NN classifier first estimates the distance between J morph and [J 1 , . . . J M ] based on Euclidean distance. The distance values are denoted as [ ⁇ d 1 , ⁇ 1 ⁇ , . . . ⁇ d M , ⁇ M ⁇ ], where
- the distances are then sorted from smallest to largest to produce [ ⁇ S 1 , ⁇ 1 ⁇ , . . . ⁇ S M , ⁇ M ⁇ ], where S 1 corresponds to the smallest distance, ⁇ 1 corresponds to the label of the smallest distance, S M corresponds to the largest distance, and ⁇ M corresponds to the label of the largest distance.
- the labels of the K smallest distances, [ ⁇ 1 , . . . ⁇ K ] are examined based on a majority vote.
- [K 1 , K 2 , . . . K C ] as a set corresponding to the number of labels in [ ⁇ 1 , . . . ⁇ K ] of each class (where a class denotes T).
- N p 1
- the adaptive KP algorithm is capable of predicting the number of clusters present in the morphological image.
- the adaptive KP algorithm reduces false alarms present in the morphological image.
- FIG. 15 is a block diagram of the adaptive KP algorithm.
- target means a person or persons, or portion thereof, animal or animals, object, or a combination thereof.
- point of interest or “points of interest” refer to an signature or area in the image which appears to be a target but may or may not be a target; i.e., potentially the point of interest may be a target; subject to further processing or testing.
- subimage or “sub image” means a portion of an image (also referred to herein as a patch), or the like.
- the “energy” corresponds to the intensity of the image pixels.
- processor includes computer, controller, CPU, microprocessor; multiprocessor, minicomputer, main frame, personal computer, PC, coprocessor, and combinations thereof or any machine similar to a computer or processor which is capable of processing algorithms.
- process means: an algorithm, software, subroutine, computer program, or methodology.
- algorithm means: sequence of steps using computer software, process, software, subroutine, computer program, or methodology.
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Abstract
Description
{dot over (f)} i,j,k(r)=f i+1,j,k(r)f i,j,k(r),i=1, . . . ,N−1,j=1, . . . ,M, and k=1, . . . ,Nc. (1)
Here r represents the downrange index, i represents the time index, j represents the transmitter index, and k represents the receiver index. Hence, a signal is formed that monitors changes between the two sets of downrange profiles measured at time i and time i+1 using transmitter j and receiver k; hence, the name of the model is a “change detection” (CD) paradigm. The difference signal, {dot over (f)}i,j,k(r) (corresponding to the derivative in time), is then input to an image formation routine, in this case a time-domain back-projection procedure, resulting in the output difference image,
where g(i,j,k) is a scaling function. To illustrate the effectiveness of the CD approach, the SAR images in
Constant False Alarm Rate (CFAR) Approach
is the sum of the energy in the inner window, k=[Y−└IY/2┘, . . . Y+└IY/2┘], l=[X−└IX/2┘, . . . X+└IX/2┘], and P(l,k) is the magnitude of the pixel at position (l,k). Define
where η=max(Idiff(x,y))/2 and max(Idiff(x,y)) is the maximum pixel magnitude in the difference image. The function Φ(P(l,k)) is used to adjust the image background and require that the magnitude of each pixel is above the threshold defined by η, which is done to prevent errors due to division by very small numbers. Division by very small numbers artificially inflates the ratio defined by
is the sum of the energy in the entire CFAR window, m=[Y−└OY/2┘, . . . Y+└OY/2┘], n=[X−└OX/2┘, . . . X+└OX/2┘], and where EI+G is defined as the sum of the energy in the guard and inner windows such that
where q=[Y−└GY/2┘, . . . Y+└GY/2┘] and r=[X−└GX/2┘, . . . X+└GX/2┘]. A CFAR test is defined as
which requires that the sum of the energy in the inner window is more than twice the sum of the energy in the outer window. If Ψ=1, then the center pixel (at coordinates (X,Y)) is a POI corresponding to an assumed moving target. The CFAR window scans the entire difference image and a list of POIs are identified. For example, consider the difference image and CFAR image of
for all j=1, . . . 484 and k=1, . . . 484. When the dilation window scans the CFAR image, an 8 pixel buffer exists along the edge of the CFAR image (i.e. not enough samples exist at the edges of the image). There exist i=1, . . . N−1 dilation images; one for each CFAR image. If Ψ=1 for a given i, j, k then a dilation occurs and Di(j+8, k+8)=1, where Di(x,y) is a dilation image of size (500×500). If Ψd=0, then Di(j+8, k+8)=0, and no dilation occurs.
and Ω=34 is the erosion threshold, j=1, . . . 484, and k=1, . . . 484. There exist i=1, . . . N−1 erosion images; one for each dilation image. If Ψe=1 for a given i, j, k, then Ei(j+8, k+8)=1, where Ei(x,y) is an erosion image of size (500×500). If Ψe=0, then an erosion occurs and Ei(j+8, k+8)=0. The set of erosion images, {E1(x,y) . . . EN-1(x,y)}, is referred to as the morphological output images.
Clustering Analysis
J={
where
where j={1, . . . C}. For the example described in the above paragraph, Np=1, meaning that the majority of training NMSOS errors indicate that the NMSOS error of Jmorph is from class T=1. The results of the research described in A. Martone, et al., “Clustering analysis of moving target signatures,” in Proceedings of the SPIE conference on Radar Sensor Technology XIV, Orlando, Fl, April 2010, indicate that the adaptive KP algorithm is capable of predicting the number of clusters present in the morphological image. Furthermore, it was shown that the adaptive KP algorithm reduces false alarms present in the morphological image.
Claims (19)
J={
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